Stochastic Dynamics of Cascading Failures in Electric-Cyber Infrastructures

Emerging smart grids consist of tightly-coupled systems, namely a power grid and a communication system. While today\u27s power grids are highly reliable and modern control and communication systems have been deployed to further enhance their reliability, historical data suggest that they are yet vulnerable to large failures. A small set of initial disturbances in power grids in conjunction with lack of effective, corrective actions in a timely manner can trigger a sequence of dependent component failures, called cascading failures. The main thrust of this dissertation is to build a probabilistic framework for modeling cascading failures in power grids while capturing their interactions with the coupled communication systems so that the risk of cascading failures in the composite complex electric-cyber infrastructures can be examined, analyzed and predicted. A scalable and analytically tractable continuous-time Markov chain model for stochastic dynamics of cascading failures in power grids is constructed while retaining key physical attributes and operating characteristics of the power grid. The key idea of the proposed framework is to simplify the state space of the complex power system while capturing the effects of the omitted variables through the transition probabilities and their parametric dependence on physical attributes and operating characteristics of the system. In particular, the effects of the interdependencies between the power grid and the communication system have been captured by a parametric formulation of the transition probabilities using Monte-Carlo simulations of cascading failures. The cascading failures are simulated with a coupled power-system simulation framework, which is also developed in this dissertation. Specifically, the probabilistic model enables the prediction of the evolution of the blackout probability in time. Furthermore, the asymptotic analysis of the blackout probability as time tends to infinity enables the calculation of the probability mass function of the blackout size, which has been shown to have a heavy tail, e.g., power-law distribution, specifically when the grid is operating under stress scenarios. A key benefit of the model is that it enables the characterization of the severity of cascading failures in terms of a set of operating characteristics of the power grid. As a generalization to the Markov chain model, a regeneration-based model for cascading failures is also developed. The regeneration-based framework is capable of modeling cascading failures in a more general setting where the probability distribution of events in the system follows an arbitrarily specified distribution with non-Markovian characteristics. Further, a novel interdependent Markov chain model is developed, which provides a general probabilistic framework for capturing the effects of interactions among interdependent infrastructures on cascading failures. A key insight obtained from this model is that interdependencies between two systems can make two individually reliable systems behave unreliably. In particular, we show that due to the interdependencies two chains with non-heavy tail asymptotic failure distribution can result in a heavy tail distribution when coupled. Lastly, another aspect of future smart grids is studied by characterizing the fundamental bounds on the information rate in the sensor network that monitors the power grid. Specifically, a distributed source coding framework is presented that enables an improved estimate of the lower bound for the minimum required communication capacity to accurately describe the state of components in the information-centric power grid. The models developed in this dissertation provide critical understanding of cascading failures in electric-cyber infrastructures and facilitate reliable and quick detection of the risk of blackouts and precursors to cascading failures. These capabilities can guide the design of efficient communication systems and cascade aware control policies for future smart grids

Computational and Analytical Tools for Resilient and Secure Power Grids

Enhancing power grids' performance and resilience has been one of the greatest challenges in engineering and science over the past decade. A recent report by the National Academies of Sciences, Engineering, and Medicine along with other studies emphasizes the necessity of deploying new ideas and mathematical tools to address the challenges facing the power grids now and in the future. To full this necessity, numerous grid modernization programs have been initiated in recent years. This thesis focuses on one of the most critical challenges facing power grids which is their vulnerability against failures and attacks. Our approach bridges concepts in power engineering and computer science to improve power grids resilience and security. We analyze the vulnerability of power grids to cyber and physical attacks and failures, design efficient monitoring schemes for robust state estimation, develop algorithms to control the grid under tension, and introduce methods to generate realistic power grid test cases. Our contributions can be divided into four major parts: Power Grid State Prediction: Large scale power outages in Australia (2016), Ukraine (2015), Turkey (2015), India (2013), and the U.S. (2011, 2003) have demonstrated the vulnerability of power grids to cyber and physical attacks and failures. Power grid outages have devastating effects on almost every aspect of modern life as well as on interdependent systems. Despite their inevitability, the effects of failures on power grids' performance can be limited if the system operator can predict and understand the consequences of an initial failure and can immediately detect the problematic failures. To enable these capabilities, we study failures in power grids using computational and analytical tools based on the DC power flow model. We introduce new metrics to efficiently evaluate the severity of an initial failure and develop efficient algorithms to predict its consequences. We further identify power grids' vulnerabilities using these metrics and algorithms. Power Grid State Estimation: In order to obtain an accurate prediction of the subsequent effects of an initial failure on the performance of the grid, the system operator needs to exactly know when and where the initial failure has happened. However, due to lack of enough measurement devices or a cyber attack on the grid, such information may not be available directly to the grid operator via measurements. To address this problem, we develop efficient methods to estimate the state of the grid and detect failures (if any) from partial available information. Power Grid Control: Once an initial failure is detected, prediction methods can be used to predict the subsequent effects of that failure. If the initial failure is causing a cascade of failures in the grid, a control mechanism needs to be applied in order to mitigate its further effects. Power Grid Islanding is an effective method to mitigate cascading failures. The challenge is to partition the network into smaller connected components, called islands, so that each island can operate independently for a short period of time. This is to prevent the system to be separated into unbalanced parts due to cascading failures. To address this problem, we introduce and study the Doubly Balanced Connected graph Partitioning (DBCP) problem and provide an efficient algorithm to partition the power grid into two operating islands. Power Grid Test Cases for Evaluation: In order to evaluate algorithms that are developed for enhancing power grids resilience, one needs to study their performance on the real grid data. However, due to security reasons, such data sets are not publicly available and are very hard to obtain. Therefore, we study the structural properties of the U.S. Western Interconnection grid (WI), and based on the results we present the Network Imitating Method Based on LEarning (NIMBLE) for generating synthetic spatially embedded networks with similar properties to a given grid. We apply NIMBLE to the WI and show that the generated network has similar structural and spatial properties as well as the same level of robustness to cascading failures. Overall, the results provided in this thesis advance power grids' resilience and security by providing a better understanding of the system and by developing efficient algorithms to protect it at the time of failure

Resilience of power grids and other supply networks: structural stability, cascading failures and optimal topologies

The consequences of the climate crisis are already present and can be expected to become more severe in the future. To mitigate long-term consequences, a major part of the world's countries has committed to limit the temperature rise via the Paris Agreement in the year 2015. To achieve this goal, the energy production needs to decarbonise, which results in fundamental changes in many societal aspects. In particular, the electrical power production is shifting from fossil fuels to renewable energy sources to limit greenhouse gas emissions. The electrical power transmission grid plays a crucial role in this transformation. Notably, the storage and long-distance transport of electrical power becomes increasingly important, since variable renewable energy sources (VRES) are subjected to external factors such as weather conditions and their power production is therefore regionally and temporally diverse. As a result, the transmission grid experiences higher loadings and bottlenecks appear. In a highly-loaded grid, a single transmission line or generator outage can trigger overloads on other components via flow rerouting. These may in turn trigger additional rerouting and overloads, until, finally, parts of the grid become disconnected. Such cascading failures can result in large-scale power blackouts, which bear enormous risks, as almost all infrastructures and economic activities depend on a reliable supply of electric power. Thus, it is essential to understand how networks react to local failures, how flow is rerouted after failures and how cascades emerge and spread in different power transmission grids to ensure a stable power grid operation. In this thesis, I examine how the network topology shapes the resilience of power grids and other supply networks. First, I analyse how flow is rerouted after the failure of a single or a few links and derive mathematically rigorous results on the decay of flow changes with different network-based distance measures. Furthermore, I demonstrate that the impact of single link failures follows a universal statistics throughout different topologies and introduce a stochastic model for cascading failures that incorporates crucial aspects of flow redistribution. Based on this improved understanding of link failures, I propose network modifications that attenuate or completely suppress the impact of link failures in parts of the network and thereby significantly reduce the risk of cascading failures. In a next step, I compare the topological characteristics of different kinds of supply networks to analyse how the trade-off between efficiency and resilience determines the structure of optimal supply networks. Finally, I examine what shapes the risk of incurring large scale cascading failures in a realistic power system model to assess the effects of the energy transition in Europe

A network approach for power grid robustness against cascading failures

Cascading failures are one of the main reasons for blackouts in electrical power grids. Stable power supply requires a robust design of the power grid topology. Currently, the impact of the grid structure on the grid robustness is mainly assessed by purely topological metrics, that fail to capture the fundamental properties of the electrical power grids such as power flow allocation according to Kirchhoff's laws. This paper deploys the effective graph resistance as a metric to relate the topology of a grid to its robustness against cascading failures. Specifically, the effective graph resistance is deployed as a metric for network expansions (by means of transmission line additions) of an existing power grid. Four strategies based on network properties are investigated to optimize the effective graph resistance, accordingly to improve the robustness, of a given power grid at a low computational complexity. Experimental results suggest the existence of Braess's paradox in power grids: bringing an additional line into the system occasionally results in decrease of the grid robustness. This paper further investigates the impact of the topology on the Braess's paradox, and identifies specific sub-structures whose existence results in Braess's paradox. Careful assessment of the design and expansion choices of grid topologies incorporating the insights provided by this paper optimizes the robustness of a power grid, while avoiding the Braess's paradox in the system.Comment: 7 pages, 13 figures conferenc